Questions on Algebra: Sequences of numbers, series and how to sum them answered by real tutors!

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Question 1209905: Fill in the blanks, to make a true equation.
3/(3^2 - 1) + 3^2/(3^4 - 1) + 3^3/(3^6 - 1) + 3^4/(3^8 - 1) + ... + 3^(2(n - 1))/(3^(2n) - 1) = ___/___

Hint: Let S_n = \frac{3}{3^2 - 1} + \frac{3^2}{3^4 - 1} + \frac{3^3}{3^6 - 1} + \frac{3^4}{3^8 - 1} + ... + \frac{3^{2(n - 1)}}{3^{2n} - 1}. Compute the first few values of S_n.
Click here to see answer by ikleyn(52788)

Question 1209977: For a positive integer n, let f(n) denote the integer that is closest to
. Find the integer m so that
.

Click here to see answer by ikleyn(52788)

Question 1209977: For a positive integer n, let f(n) denote the integer that is closest to
. Find the integer m so that
.

Click here to see answer by Edwin McCravy(20056)

Question 1168320: Suppose the yearly inflation rate from 2014 to 2020 is 15%, the table that costs $800 at the start of 2014 costs $920 at the start of 2020, and so on. What equation represents the cost of the table from the year 2014 to 2020?
Click here to see answer by ikleyn(52788)

Question 1169051: The sample of work produced by lathe is 10000.
a. If the machine doubled this production every 20 minutes, how much will it produce
in one hour?
b. How long will it take the machine to produce 8 million?
Click here to see answer by CPhill(1959)

Question 1210195: If a,b,c are in Harmonic Progression,prove that 1/a + 1/(b+c), 1/b + 1(c+a), 1/c + 1(a+b) are also in Harmonic Progression
Click here to see answer by mccravyedwin(407)

Question 1168274: what is the first five terms and 50th term of this sequence.
An=2a n-1 + 5 and a1=3
Click here to see answer by ikleyn(52788)

Question 1168274: what is the first five terms and 50th term of this sequence.
An=2a n-1 + 5 and a1=3
Click here to see answer by greenestamps(13200)

Question 1168274: what is the first five terms and 50th term of this sequence.
An=2a n-1 + 5 and a1=3
Click here to see answer by Edwin McCravy(20056)

Question 1210209: If a,b,c are in Harmonic Progression, show that 1/a + 1/(b+c) , 1/b + 1/(c+a) , 1/c + 1/(a+b) are also in Harmonic Progression
Click here to see answer by CPhill(1959)

Question 1210233: Show that the sum of n terms of the progression
log(x), log(x^2), log(x^3), log(x^4) , ..., log(x^n) is (n*(n+1)/2)*log x.
Click here to see answer by Edwin McCravy(20056)

Question 1210233: Show that the sum of n terms of the progression
log(x), log(x^2), log(x^3), log(x^4) , ..., log(x^n) is (n*(n+1)/2)*log x.
Click here to see answer by ikleyn(52788)

Question 1210233: Show that the sum of n terms of the progression
log(x), log(x^2), log(x^3), log(x^4) , ..., log(x^n) is (n*(n+1)/2)*log x.
Click here to see answer by mccravyedwin(407)

Question 1179819: f. Find the present values of the following annuities
i. RM6,000 every year for 8 years at 12% compounded annually
ii. RM800 every month for 2 years 5 months at 5% compounded monthly

Click here to see answer by ikleyn(52788)

Question 1209805: Let a_1 + a_2 + a_3 + dotsb be an infinite geometric series with positive terms. If a_2 = 10, then find the smallest possible value of
a_1 + a_2 + a_3.
Click here to see answer by ikleyn(52788)

Question 1209827: Find a closed form for
S_n = 1! \cdot (1^2 + 1) + 2! \cdot (2^2 + 2) + \dots + n! \cdot (n^2 + n).\]
for any integer n \ge 1. Your response should have a factorial.
Click here to see answer by ikleyn(52788)

Question 1209826: For a positive integer k, let
S_k = 1 \cdot 1! \cdot 2 + 2 \cdot 2! \cdot 3 + \dots + k \cdot k! \cdot (k + 1).
Find a closed form for S_k.
Click here to see answer by ikleyn(52788)

Question 1210345: THE 2ND AND 7TH TERM OF A G.P ARE 18 AND 4374 RESPECTIVELY. FIND THE
1) COMMON DIFFERENCE
2) FIRST TERM
3) SUM OF THE 4TH AND 8TH TERM
4) SUM OF THE FIRST 10 TERMS
Click here to see answer by josgarithmetic(39618)

Question 1210385: 1, 2, 4, 8, 16, 32
Please enter integer sequence
Click here to see answer by Edwin McCravy(20056)

Question 1210385: 1, 2, 4, 8, 16, 32
Please enter integer sequence
Click here to see answer by mccravyedwin(407)

Question 1210386: 1, 2, 0, 3, -1, 4, -2
Please enter integer sequence
Click here to see answer by Edwin McCravy(20056)

Question 1210386: 1, 2, 0, 3, -1, 4, -2
Please enter integer sequence
Click here to see answer by mccravyedwin(407)

Question 1210386: 1, 2, 0, 3, -1, 4, -2
Please enter integer sequence
Click here to see answer by AnlytcPhil(1806)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790